At the core room with the fan, switch to power formation and fly up to the door by it. Defeat the magician enemy and break all 3 walls even the one for the switch to open the door above it.
Grind on the left one to the pulley to head up through the hole and head upstairs. Touch the right teleporter to the 2nd room of the area and climb up the plates to reach the point to the teleporter leading to the 3rd room with spiderweb. After landing onto the wooden bridge, touch the checkpoint and defeat the enemy to open the path to the 3 skeleton rooms with one of them with the sky background outside. This time you don't necessarily need to jump to avoid these obstacles when going that fast. The less time you make it, the more chance a bonus may occur such as getting a power up for specific formation used before riding it. When you see a laser and some ghosts in the way, jump above them until you reach the digger tunnel. Climb up the steps and there's a bobsled leading through the digger tunnel. Defeat all 3 of these enemies with Power Formation and head down the pit by either using the pole or going down alone. Switch to Fly Formation and fly on top of the floating weight crusher and touch the checkpoint before touching the switch to open the door and just simply head to the teleporter beyond the lasers where it takes you to an open picture frame with the Egg Hammer in it. Once open, teleport to the room where the door is connected with walls and destroy the robots on the other side. Be sure to avoid the pumpkin ghosts while doing this. Open the closed case with the switch covered with boxes (which need to be broken in-order to activate that switch). Break it with Knuckles and the other one at the other side of the ghost upstairs too. While being inside the castle, take out the enemies near by the switch target and the other one that keeps the door closed.